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NORMALLY ORDERED SEMIGROUPS

Published online by Cambridge University Press:  01 May 2008

VÍTOR H. FERNANDES
VÍTOR H. FERNANDES*
Affiliation:
Departamento de Matemática, F.C.T., Universidade Nova de Lisboa, 2829-516 Monte da Caparica, Portugal; also: Centro de Álgebra, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1649-003 Lisboa, Portugal; e-mail: vhf@fct.unl.pt
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Abstract

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In this paper we introduce the notion of normally ordered block-group as a natural extension of the notion of normally ordered inverse semigroup considered previously by the author. We prove that the class NOS of all normally ordered block-groups forms a pseudovariety of semigroups and, by using the Munn representation of a block-group, we deduce the decompositions in Mal'cev products NOS = EIPOI and NOS ∩ A = NPOI, where A, EI and N denote the pseudovarieties of all aperiodic semigroups, all semigroups with just one idempotent and all nilpotent semigroups, respectively, and POI denotes the pseudovariety of semigroups generated by all semigroups of injective order-preserving partial transformations on a finite chain. These relations are obtained after showing the equalities BG = EIEcom = NEcom, where BG and Ecom denote the pseudovarieties of all block-groups and all semigroups with commuting idempotents, respectively.

Keywords

20M0720M1820M20
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 50 , Issue 2 , May 2008 , pp. 325 - 333
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

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